Investigating thermal transport at the Cu/Si interface holds significant importance, as understanding interface thermal conductance is crucial for enhancing materials interface thermal management, designing thermal interface materials, and improving the performance of thermoelectric devices. In this study, we conducted molecular dynamics simulations in conjunction with the Green–Kubo relation to calculate the thermal conductance of the Cu/Si interface. We successfully obtained Cu/Si interface potentials using the lattice inversion method. Our findings revealed that the thermal conductance of the Cu/Si interface is notably influenced by the interface structure. Specifically, the thermal conductance of the Cu(001)/Si(001) interface and the Cu(111)/Si(111) interface are similar, and both are higher than that of the Cu(110)/Si(110) interface. Furthermore, through first-principles calculations of the adhesion energy, we discovered that interface binding strength plays a critical role in determining interface thermal transport properties, and the influence of pressure was also discussed. This study contributes not only to the understanding of the thermal transport mechanisms at the Cu/Si interface but also provides important insights for designing novel interface materials.